God, keep me from harm and working on FPUs
The problem lies in guys like me having to make transistors give you an answer in a small amount of time and guys like him expecting results regardless of how long it would take. Intel have now sensibly fixed the documentation to explain what really happens.
Intel's PI is 66 bits and Bruce is asking for sin(0.0000001) where the number of zeroes is about 80 bits. Not suprisingly the answer is correct to 0.000001 (65 bits of zero) but huge relative to 0.00001(80 bits of zero)